Results 1 to 3 of 3

Math Help - Functions

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    7

    Functions

    Hey guys im preparing for a math contest and would like to understand how to do these questions. if anyone has any ideas please let me know.
    thanks.
    Attached Thumbnails Attached Thumbnails Functions-139-1516.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by ballaholic8 View Post
    Hey guys im preparing for a math contest and would like to understand how to do these questions. if anyone has any ideas please let me know.
    thanks.
    to #16.

    There are 2 different ways:

    1. Use implicite differentiation:

    x^2+y^2=25~\implies~2x+2y\cdot y'=0

    Plug in the coordinates of the tangent point and solve for y':

    8-6\cdot y'=0~\implies~y'=\dfrac43

    Therefore the equation of the tangent is

    y+3=\dfrac43(x-4)~\implies~\boxed{y=\dfrac43x-\dfrac{25}3}

    2.  x^2+y^2=25 is the equation of a circle with the center at the origin and with a radius of 5. The direction from the center to the tangent point is:

    m=\dfrac{-3}4 The direction of the tangent must be perpendicular to this direction and therefore

    m_t=-\dfrac1{-\frac34} = \dfrac43

    Use the point-slope-formula of a straight line to get the equation of the tangent.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    7
    any ideas to 15?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 15th 2010, 05:50 PM
  2. Replies: 3
    Last Post: February 23rd 2010, 04:54 PM
  3. Replies: 11
    Last Post: November 15th 2009, 11:22 AM
  4. Replies: 7
    Last Post: August 12th 2009, 04:41 PM
  5. Replies: 1
    Last Post: April 15th 2008, 09:00 AM

Search Tags


/mathhelpforum @mathhelpforum